A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles
微分几何
2018-12-14 v3 代数几何
摘要
This paper describes how, in the case of algebraic surfaces, the well-known theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized 'multiplier ideal sheaves', following the ideas of Siu. The key concept is that the destabilizing sheaf satisfies a differential inclusion relation. This relation is used, together with a complex Frobenius theorem for locally finitely generated subsheaves, to imply coherence of the destabilizing subsheaf.
引用
@article{arxiv.math/0306073,
title = {A complex Frobenius theorem, multiplier ideal sheaves and Hermitian-Einstein metrics on stable bundles},
author = {Ben Weinkove},
journal= {arXiv preprint arXiv:math/0306073},
year = {2018}
}
备注
21 pages; correction to statement and proof of C^{\infty} part of complex Frobenius; rest unchanged